Electronic synthesis of lightKATJA BEHA, DANIEL C. COLE, PASCAL DEL’HAYE, AURÉLIEN COILLET, SCOTTA. DIDDAMS, AND SCOTT B. PAPP*Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA*Corresponding author: scott.papp@nist.gov

Received 26 December 2016; revised 28 February 2017; accepted 28 February 2017 (Doc. ID 283589); published 27 March 2017

We report on bidirectional frequency conversion between the microwave and optical domains using electro-optics.Advances in communications, time keeping, and quantum sensing have all come to depend upon the coherent in-teroperation of light wave and microwave signals. To connect these domains, which are separated by a factor of10,000 in frequency, requires specialized technology that has until now only been achieved by ultrafast mode-lockedlasers. In contrast, electro-optic modulation (EOM) combs arise deterministically by imposing microwave-rate os-cillations on a continuous-wave laser. Here we demonstrate electro-optic generation of a 160 THz bandwidth super-continuum and realize f -2f self-referencing. Coherence of the supercontinuum is achieved through optical filteringof electronic noise on the seed EOM comb. The mode frequencies of the supercontinuum are derived from theelectronic oscillator and they achieve <5 × 10−14 fractional accuracy and stability, which opens a novel regimefor tunable combs with wide mode spacing apart from the requirements of mode locking.

OCIS codes: (230.2090) Electro-optical devices; (320.6629) Supercontinuum generation; (120.3940) Metrology; (140.3425) Laser

stabilization.

https://doi.org/10.1364/OPTICA.4.000406

1. INTRODUCTION

Optical frequency combs, precise rulers for measuring and con-trolling light waves, are now an important tool in modern scienceand technology. The key feature frequency combs provide is aphase-coherent link between optical and microwave frequenciesthrough self-referencing [1,2]. Combs enable diverse applications,including measurement of optical clocks [3]; precise calibrationfor optical spectroscopy [4], molecular identification [5], and co-herent imaging [6]; control of quantum systems [7]; carrier-phasecontrol in ultrafast science [8]; and photonic generation of micro-wave signals [9]. Existing self-referenced frequency comb technol-ogy is based either on mode-locked lasers or Kerr solitongeneration in microcombs [10,11]. Combs based on mode-lockedlasers mostly operate at fixed <1 GHz pulse repetition rate, whilemicroresonator combs offer much larger mode spacings (tens tohundreds of GHz), with values rigidly fixed by platform geom-etry. However, an emerging class of novel applications for combs,including coherent light wave communications [12], multiheter-odyne optical detection [13–15], optical waveform synthesis [16],frequency calibration, and searches for exoplanets [17], calls for acoincidence of wide tunability and pulse rates at tens of GHzor higher. These are already some of the established featuresof electro-optic modulation (EOM) combs in which the modesare derived electronically, but the central outstanding question iswhether they can support coherent optical-microwave conversion.

Before the introduction of mode-locked-laser frequencycombs, a leading approach to comb generation was directEOM of CW light [18,19]. In such an EOM comb [20–23],

the frequency of each comb mode (counted n from the CW laser)is νn � νp � nf eo and arises jointly from the CW-laser frequencyνp and frequency multiplication of the microwave modulationf eo. The relative phases of comb lines are derived from the modu-lation index apart from any mode-locking mechanism; hence, themodulation deterministically transforms a CW laser into a train oflight pulses. Furthermore, EOM-comb generators are alreadycommercialized and can be straightforwardly reconfigured bysimply changing the laser or modulation frequencies. Despitethe simplicity of EOM frequency combs, they have not yet beendeveloped into self-referenced frequency combs.

Here, we accomplish electronic synthesis of light with anEOM comb by identifying and solving two major scientific chal-lenges: low spectral broadening efficiency associated with narrowEOM-comb bandwidth and microwave repetition rates, and fullconversion of electronic noise to the optical comb that progres-sively degrades as n2 the first-order optical coherence of the comblines. Our approach multiplies the frequency of a 10 GHz oscil-lator to create an effective optical frequency reference for the193 THz CW laser at the center of the EOM comb. We imple-ment frequency multiplication both with linear EOM-comb gen-eration and with nonlinear-fiber spectral broadening. An opticalfilter cavity sufficiently reduces the fundamental electro-opticnoise of the comb to preserve its coherence.

The carrier-envelope offset frequency of an EOM comb isf 0 � νp − Nf eo, whereby a multiplicative factorN ∼ 19; 340 re-lates the exact phase of the electronic oscillator to that of the CWlaser. The need for optical filtering arises since microwave oscil-lators, given their thermal phase noise, do not support frequency

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multiplication to the optical domain [12,24,25]. Optical filteringreduces the impact of high-frequency oscillator noise and modi-fies the phase noise Fourier-frequency dependence to 1∕f 2,which is consistent with that of a laser.

To understand the filter cavity’s effect, we note that thesolution of the integral equation [26]

R 2πf eo∕2δω S�N �

ϕ F�ω�dω � 1

estimates the linewidth δω�N � of the N th EOM-comb mode.Here we focus on the limiting case for an EOM-comb mode withphase noise S�N �

ϕ � N 2Sϕ, where Sϕ is a constant microwave os-cillator spectrum and F�ω� is the filter cavity lineshape that weapproximate as a rectangle. Even for a state-of-the-art 10 GHzoscillator with thermally limited phase noise of −189 dBc∕Hzat �12 dBm at 300 K without filtering, the comb lines neededfor self-referencing are estimated to have δω�19 340�∕2π > 1 GHzand are practically undetectable. By use of an optical cavityfollowing EOM-comb generation, we sufficiently reduce thecontribution from oscillator phase noise. The result is a negligibleprojected linewidth contribution to the EOM-comb modesneeded for self-referencing.

2. EXPERIMENTAL STUDIES

A. EOM Frequency Comb Generation

Our EOM-comb system (Fig. 1) begins with a 1550 nm CWlaser that is for convenience stabilized to a high-finesse, low-expansion Fabry–Perot cavity. A frequency comb is derived byway of optical phase and intensity modulation with waveguidelithium-niobate devices at modulation frequency f eo that

transforms the CW laser into light pulses repeated with eachmodulation cycle [27–29]. The resulting linear chirp yields pulseswhose spectral envelopes are relatively flat, as shown in Figs. 1(a)and 1(c), for combs with 10 and 33 GHz spacing, respectively.Still, the bandwidth of these combs is <1 THz, a factor of 200too small for self-referencing. Subsequent spectral broadening ofthe EOM comb exploits the fact that its spectral-phase profilecan be compensated using just second-order dispersion [30].Propagation of the 50% duty cycle pulse train through an appro-priate length of 1550 nm single-mode fiber (SMF) allows pulsecompression to 1.7 ps, which is near the Fourier-transform limit.

To increase the EOM-comb bandwidth for self-referencing,we utilize two stages of spectral broadening [31] in commerciallyavailable highly nonlinear fiber (HNLF). In contrast to earlier re-sults obtained with sub-40-fs titanium–sapphire mode-lockedpulses [32], our work opens a new regime in which we realizecoherent, octave-spanning frequency combs seeded by relativelylong optical pulses. In the first broadening stage, we amplify theEOM comb to 500 mW using a commercial erbium-doped fiberamplifier. Next, the light is guided through a 100 m length ofnear-zero-dispersion HNLF. The resulting optical spectrum ischaracteristic of self-phase modulation (SPM); Fig. 1(b) showsthe 10 GHz comb following the first broadening stage. In thecase of the 33 GHz EOM comb, we show the use of line-by-linepower flattening with a spatial light modulator after the SPMbroadening [see Fig. 1(d)].

B. Supercontinuum Generation

Our second broadening stage is designed to coherently increasethe EOM-comb span to the >1000 nm needed for f -2f self-ref-erencing. Operationally, as shown in Fig. 1, the EOM comb lightis reamplified with a cladding-pumped, anomalous dispersion Er/Yb co-doped fiber to yield 140, 400, and 560 pJ pulses for the 33,10, and 2.5 GHz EOM comb repetition frequencies, respectively.The 2.5 GHz comb is obtained by attenuating three out of everyfour 10 GHz pulses using a waveguide lithium-niobate intensitymodulator [8,21,33,34]. The Er/Yb amplifier offers a maximumaverage power of 4.5 W, while the temporal intensity autocorre-lation of optical pulses exiting the amplifier exhibits <300 fs du-ration. Prior to the second-stage amplifier, we adjust both thepolarization and dispersion of the second stage to maximize super-continuum generation in HNLF-2. Specifically, second-orderdispersion is applied in increments of 0.005 ps2 using theline-by-line pulse shaper.

The design and implementation of coherent supercontinuumgeneration at high repetition rate is an advancement of our work.HNLF-2 is composed of two segments of nonlinear fiber withdifferent spectral-dispersion profiles. These are fusion-spliced to-gether with >80% transmission. The first segment has a zerodispersion point near 1300 nm that explains the dispersive wavecentered at 1100 nm in Figs. 2(b) and 2(c). The dispersion of thesecond segment is 1.5 ps/(nm-km), and this fiber generates a dis-persive-wave pattern near 1200 nm and broad supercontinuumpeaks near 2100 nm. We largely avoid supercontinuumdecoherence mechanisms previously associated with >100 fspulse duration [35]. Figure 2 shows particular examples of theultrabroad spectra we obtain with our EOM comb. The 10and 2.5 GHz cases feature more than one octave of bandwidth,and the 10 and 33 GHz comb teeth are prominent across the

Fig. 1. Apparatus for self-referencing a CW laser. The system is com-prised of electro-optic phase and intensity modulators, two stages of non-linear-fiber (HNLF-1 and -2) spectral broadening, a Fabry–Perot opticalcavity filter, and f − 2f detection. (a) EOM comb with 10 GHz spacing.(b) Idem after HNLF-1. (c) EOM comb with 33 GHz spacing. (d) Idemafter HNLF-1 and line-by-line intensity control.

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entire spectra. (Optical-spectrum-analyzer resolution preventsobservation of the 2.5 GHz spaced teeth.)

C. Carrier-Envelope-Offset-Frequency Detectionof an EOM Comb

Following supercontinuum generation, we detect the carrier-envelope-offset frequency (f 0) of the EOM comb. A 10 mmsample of periodically poled lithium niobate generates the secondharmonic of supercontinuum light at 2140 nm; Fig. 3(a) showsseparately obtained optical spectra of the f and 2f components at1070 nm for the 2.5 GHz comb. We photodetect the opticalheterodyne beat of these two spectra and optimize alignmentof their relative arrival time and polarization. The photocurrentreveals the offset frequency f 0 of an EOM comb. This signal rep-resents the generation of an effective optical frequency referencethrough extreme multiplication of the microwave f eo; Fig. 3(b)shows the RF spectrum of the offset beat f 0. We have not beenable to detect f 0 with the filter cavity removed from the system.This Fabry–Perot optical cavity, which includes a mechanicaltranslation stage to match the FSR to f eo, features a 7 MHzFWHM linewidth, a ∼10 GHz FSR directly locked to νpby feedback to its length, and an insertion loss of 8 dB for theentire SPM-broadened EOM comb. Our unsuccessful searchfor f 0 without the filter cavity involves careful re-optimizationof the pulse shaper dispersion setting and all other relevantsystem parameters. The procedure yields f and 2f supercontin-uum components comparable to those shown in Fig. 3(a).(Furthermore, we use the highest-performance f eo oscillator avail-able; see our discussion of the sapphire device.) This matches ourexpectation that the supercontinuum coherence is severely

degraded by frequency multiplication of oscillator thermal phasenoise, which sits between the modes of the EOM comb. We didnot explore placing the filter cavity before HNLF-1 because thedispersion properties of our cavity allow transmission of the com-plete SPM comb, but future exploration could consider such anarrangement. Future work should consider mode-pulling effectsrelated to the filter cavity, which can be reduced by noisecancelling [36].

We characterize f 0 in detail to understand the potentialfor precision optical measurements with an EOM comb.Electronic spectrum analyzer traces of the 2.5 GHz comb f 0

beat and its background contributions are shown in Fig. 3(b);the black trace (i) is the signal, and the red (ii) and gray (iii) tracesrepresent the supercontinuum intensity noise and photo-detector noise, respectively. [Fig. 3(c) shows the 10 GHzcase, without pulse picking.] Since the EOM comb spacingf eo � 9.999 952 GHz is locked to a hydrogen-maser frequencyreference traceable to the International System second, detectingthe center of the f 0 spectrum represents an absolute determina-tion of νp. Frequency-counting experiments with f 0 are enabledby a high signal-to-noise ratio (SNR) and narrow spectral width.The noise floor of f 0 exceeds the intensity noise by 8 dB. Atpresent, we cannot determine the relative contributions to thisnoise floor of supercontinuum generation, which often inducesphase noise in f 0 [35,37], and electronic noise that is not suffi-ciently attenuated by the filter cavity. Still, as we show later, theoffset beat we obtain is adequate to establish a phase-coherent linkbetween the microwave and optical domains.

The linewidth of f 0 is an important consideration for futureapplications. Previous work has analyzed the relationship betweena laser’s linewidth and its phase-noise spectrum [38–40]. Buildingon Ref. [40], we would expect that the EOM comb f 0 linewidthis largely determined by the level of f eo phase noise atFourier frequencies from approximately 10 kHz–10 MHz.

Fig. 2. Supercontinuum generated using our second broadening stagewith HNLF-2. (a) EOM-comb spacing is 33 GHz. (b) Idem but for10 GHz spacing. (c) Pulse picking prior to HNLF-2 reduces the initialspacing to 2.5 GHz.

Fig. 3. EOM-comb offset-frequency detection. (a) Spectra of funda-mental and second-harmonic supercontinuum light at 1070 nm.(b) i, Carrier-offset heterodyne beat (f 0) in black; ii, intensity noisein red; iii, detector noise in gray. (c)–(e) Spectrum of f 0 with differentf eo sources, including a synthesizer, dielectric-resonator oscillator, andsapphire-cavity oscillator. The 2.5 GHz cases utilize pulse picking.All the photocurrent spectra are acquired with 100 kHz bandwidth,and frequency axes are offset 706.6, 1793, 491, and 726 MHz, respec-tively, in (b)–(d).

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(The filter cavity reduces >3.5 MHz noise.) In this range, a highmodulation index leads to the most significant f 0 broadening.To directly explore this concept with the EOM comb, we recordthe power spectrum of f 0 using three separate f eo oscillators,which have different 10 kHz–10 MHz phase-noise levels.Figures 3(c)–3(e) are acquired using f eo oscillators withimproving phase-noise performance: the same synthesizer as justdiscussed but excluding pulse picking, a 10 GHz dielectric-resonator oscillator (DRO), and a 10 GHz sapphire-cavity oscil-lator (sapphire), respectively.

The data traces in Figs. 3(c)–3(e) indicate up to a factor of40 reduction in linewidth to ∼100 kHz with improved f eoperformance, which roughly corresponds to the phase-noisespecification of these devices. In particular, since pulse pickingonly divides the pulse-repetition rate, we expect and observeno linewidth change when using the synthesizer for the 10and 2.5 GHz combs. Our f 0 linewidth measurements suggestthe DRO (sapphire) devices feature a 10 kHz–10 MHz inte-grated phase noise at least a factor of ∼9�∼2200� lower thanthe synthesizer. Moreover, the filter cavity was included in thesetup for these measurements; hence, they highlight therole of frequency-dependent f eo phase noise apart frombroadband thermal noise. Future experiments utilizing ultra-low-noise microwave references could realize a <100 kHzlinewidth f 0 beat that is competitive with some mode-lockedlasers [41,42].

D. Electronic Measurement and Synthesis of anOptical Frequency

Access to the offset frequency of the EOM comb enables precisionexperiments, including measurement and synthesis of opticalfrequencies. The schematic in Fig. 4(a) summarizes the opticaland electronic connections for our experiments with the synthe-sizer-driven comb. By measuring f 0 with an Agilent 53230Afrequency counter, we determine νp with respect to theEOM-comb spacing. The counter records f 0 after RF filteringand digital frequency division, which phase-coherently reducefluctuations. Each 1 s measurement yields νp with a fractionaluncertainty of 3 × 10−13. As a crosscheck and for comparison, weobtain a separate measurement of νp with respect to the250.32413 MHz spacing of a self-referenced erbium-fiber fre-quency comb. Both the EOM-comb and the fiber-comb spacingsare referenced to the same hydrogen maser. Figure 4(b) shows arecord over 4000 s, during which we monitor the CW laser fre-quency with the EOM comb (black points) and fiber comb (greenpoints). This data tracks the approximately 65 mHz/s instanta-neous linear drift rate of the cavity-stabilized νp. Moreover, linearfitting of the two data sets reveals an average offset between themof 17 Hz, which is less than 2 standard deviations of the mean oftheir combined uncertainty. This represents the accuracy level, interms of environmental fluctuations that exceed the SNR limits ofour digital frequency counting, which our EOM comb systemachieves with <22 dB SNR in f 0 [43]. Operating the comb withthe DRO and sapphire oscillator yield improved results, asexpected from their increased SNR.

To understand the precision of such optical frequency-counting measurements, we present their Allan deviation inFig. 4(c). For less than 100 s averaging, both the EOM and fibercomb instabilities are consistent with their common referencemaser’s instability of 3 × 10−13∕

ffiffiffiτ

p, where τ is the averaging time.

Beyond τ ∼ 100 s the drift rate of νp, indicated by the solid line,becomes apparent. By post-correcting the two datasets with thefitted drift rates, the fractional instability reduces to 3 × 10−14 at1000 s and represents the uncertainty in our determination of themeans of the two sets. By comparing νp and f eo of the comb at theinput and output of our entire system, we deduce that the near1 km fiber length of the system contributes to the uncertainty atapproximately this level.

Finally, we stabilize the frequency νp of the CW laser using anRF phase-lock of f 0 while f eo is held fixed at 9.999 952 GHz.

Fig. 4. Demonstration of optical frequency measurements and synthe-sis. (a) System components and connections. Both the EOM comb andan auxiliary fiber comb are referenced to a hydrogen maser. (b) Frequencycounting record over 4000 s of the pump laser νp with the EOM (blackpoints) and fiber (green circles) combs. (c) Allan deviation of thefrequency count record from (b) for EOM comb (black points) andfiber comb (green circles) and the synthesis data (green points) in (d).The solid line indicates the Allan deviation of a 193 THz laser driftingat 65 mHz/s. (d) Phase-lock synthesis of νp with respect to themaser-referenced f eo; νset � 193 397 334 972 kHz. Green points aremeasurements of locked νp with the fiber comb, and blue points arethe in-loop noise.

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Operationally, we phase-coherently filter f 0 and divide it by 512prior to discrimination with a digital phase-frequency detector,and feedback with <1 kHz bandwidth is provided to anacousto-optic frequency modulator immediately following theCW laser. The phase-noise spectrum of f 0 (see Fig. S5 inSupplement 1) is not substantially changed but the slow driftof νp is reduced. This represents an optimization of our systemin which the cavity-stabilized pump laser is much more spectrallypure (but less stable long term) than the effective opticalfrequency of the multiplied f eo. To verify the phase lock,Fig. 4(d) presents two consecutively obtained frequency-countingmodalities with νp: fiber comb measurements (green points) andin-loop fluctuations in the νp phase lock (blue points). In theseexperiments, the set point of the νp phase lock is held constant atprecisely 193.397 334 972 THz, but this value is adjustablewithin the CW fiber laser’s tuning range of ∼30 GHz aboutthe 1.5 GHz FSR modes of the optical reference cavity. The datais semi-continuously acquired at 1 s gate time for 2000 s, as wereconfigure system connections and slightly adjust the phase-lockloop filter. The mean difference of the green points and the phase-lock setpoint is −14�8� Hz, while the frequency offset of the in-loop signal scatters closely about zero. Furthermore, the Allandeviation of the locked νp is presented alongside previously de-scribed data in Fig. 4(c). Here the solid green points fall slightlybelow the other two Allan deviation measurements and do notshow the 65 mHz/s cavity drift, since all system componentsare phase-locked to the same maser reference. This demonstratesthe capability to directly synthesize with respect to the maser ofthe optical frequency of every EOM-comb line.

3. CONCLUSION

We have demonstrated optical frequency synthesis and control ofa CW laser by way of electro-optic modulation. To accomplishthis, we form an EOM comb with 600 GHz initial bandwidth,and then use HNLF-based spectral broadening to create an oc-tave-spanning supercontinuum. A second advancement of ourwork is the demonstration of optical filtering to preserve the op-tical coherence of the EOM comb following frequency multipli-cation from 10 GHz to 193 THz. We demonstrate both precisionoptical frequency measurements and phase-locked synthesis of allthe comb frequencies. These capabilities have already matured inthe mode-locked-laser platform. Nevertheless, EOM combs offerimportant advantages, including wide microwave-rate mode spac-ing, frequency tuning of the comb, and already-commercializedcomponents that immediately lead to robust systems for a varietyof applications in spectroscopy, astronomy, and communications.

Funding. Air Force Office of Scientific Research (AFOSR)(FA9550-16-1-0016); Defense Advanced Research ProjectsAgency (DARPA); National Aeronautics and SpaceAdministration (NASA); National Science Foundation (NSF)(DGE 1144083).

Acknowledgment. We thank L. Sinclair and E. Lamb forhelpful comments on the manuscript, M. Hirano for providingthe HNLF, F. Baynes and F. Quinlan for the cavity-stabilizedlaser, and A. Hati for providing the sapphire oscillator.

See Supplement 1 for supporting content.

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